I plucked some bits and pieces out of the Stellarium source code and built myself a planetary conjunction finder, looking for times when planet A is at inferior conjunction as seen from planet B. Specifically, I was looking for transits. Sure enough, I found what is apparently the rarest transit of all: a transit of Uranus as seen from Neptune.

It's a picture-perfect transit. The center of Uranus passes a bit more than 2" from the center of the Sun; it looks like a little black bulls-eye at the mid point. With 43 hours between first and fourth contact, Neptune makes almost three rotations during the transit.

And maybe at 6 August 46,915 23:14 UTC we'll have an outpost or two on the moons of Neptune that can actually image this transit.

Since I don't expect to live quite that long, I'd like to know how accurate the VSOP87 model is over such a vast expanse of time. How confidently can I say that Uranus will actually transit the Sun, as seen from Neptune, at that time?

I think I remember hearing hundreds of years for both VSOP and numerical methods. There is too much chaos to trust the results beyond that. Once your semi-major axis has a small amount of error in it, your period has a small amount of error, resulting in error in the placement of the planet on its orbit. This error accumulates orbit after orbit.

Your result isn't completely meaningless, though. You've demonstrated that Uranus transits from Neptune are rare, happening on timescales in the tens of thousands of years.

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By your calculations...When was the last time this transit happened?

March 1, 20,807 BCE. Searches farther forward, up to about 300,000 CE, reveal transits at roughly 50,000 to 70,000 year intervals. I haven't looked farther backward.

Stellarium, as released, doesn't work too smoothly with JDs less than zero; the JD-to-calendar conversion seems to assume that float-to-integer conversion always rounds down, when in C++ such conversion rounds toward zero. I plan to submit a patch Real Soon Now.